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Lennard-Jones 6-12 potential

  1. Mar 7, 2013 #1
    1. The problem statement, all variables and given/known data
    Deduce the form of the Lennard-Jones potential between two water molecules.

    given/known:
    molar enthalpy of evaporation of water is 4.1x104J/mol
    density is 103kg/m3
    Assume water molecule is surrounded by approximately ten nearest-neighbours.
    Take Mr = 18

    2. Relevant equations

    from the sources i have:
    V(r)=4ε[-(σ/r)6+(σ/r)12]

    3. The attempt at a solution

    ε is a measure of how strongly the molecules attract each other.
    σ is the distance at which the intermolecular potential is zero.
    r is the distance of seperation between both particles.

    its a bit unclear what the question means by "deduce the form" but im assuming it means find the value r.

    to find r i first find the atomic diameter d= [(Mr(X)x10-3)/(pNA)]1/3

    where X is number of molecules
    Mr = 18
    p given at 103kg/m3
    NA is avogadros constant.

    and X im unsure if it is 2 (because the question says two molecules) or if its 11 (because of the molecule plus its 10 "neighbours")

    if X is 2 i get a diameter of 1.815x10-10
    giving a radius of 9.07x10-11

    if X is 11 i get d = 3.20x10-10
    making r = 1.60x10-10

    now to get the "form" i just sub an r into the potential equation??

    however, i dont entirely understand the "ten nearst-neighbours" and what its used for.
    i also dont use the molar enthalpy.
    molar enthalpy isnt mentioned anywhere in my notes but online it says enthlpy is a measure of energy of the system.

    some clarification would be much appreciated
    thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 8, 2013 #2
    kept at it and found

    molecular enthalpy of sublimation Hm.s = 1/2(nNAΔE)
    where n is the number of "nearest neighbours"
    solving for ΔE i got 1.36x10-20 J which seems appropriate.

    and ΔE = ε when r is at equilibrium distance.

    so subbing that back into the lennard-jones and simplifying i get

    5.44x10-20[-(σ/0.72x10-10)6+(σ/0.72x10-10)12]

    is that meant to be "the form of the Lennard-Jones 6-12 potential" that the question says deduce?
     
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